# The perimeter of triangle ABC is 85. Side AB is 15 cm less than side BC, and side AC is 22

**The perimeter of triangle ABC is 85. Side AB is 15 cm less than side BC, and side AC is 22 cm larger than AB. Find the length of side BC.**

Let the length of the BC side of the ABC triangle be x cm. The AB side of this trackball is 15 cm less than the BC side and is equal to (x – 15) cm.The AC side is 22 cm larger than the AB side and is equal to (x – 15 + 22) cm. The perimeter of the triangle is equal to the sum of the lengths of its three sides and, according to the problem statement, is equal to (x + (x – 15) + (x – 15 + 22)) cm or 85 cm. Let’s make an equation and solve it.

x + (x – 15) + (x – 15 + 22) = 85;

x + x – 15 + x – 15 + 22 = 85;

3x – 8 = 85;

3x = 85 + 8;

3x = 93;

x = 31 (cm) – BC length.

Answer. The BC side of the ABC triangle is 31 cm.